ASIDE: Each nickel is worth 5 cents ($0.05) and each quarter is worth 25 cents ($0.25)

Let n = the number of nickels in the purse
This means (30-n) = the number of quarters in the purse (since there is a total of 30 COINS)

Since each nickel is worth 5 cents, we know that n nickels is worth 5n CENTS
Likewise, since each quarter is worth 25 cents, we know that (30-n) quarters is worth 25(30-n) CENTS

The total value of all coins in the purse is $ 4.70
We can also say that the TOTAL value is 470 CENTS
So, we can write: (value of all nickels) + (value of all quarters) = 470 CENTS
Or: 5n + 25(30-n) = 470
Expand: 5n + 750 - 25n = 470
Simplify: -20n + 750 = 470
Subtract 750 from both sides: -20n = -280
Solve: n = 14

Answer: B

Cheers,
Brent
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To frame this as an equation:

n = number of nickels
q = number of quarters

1) \(.25q + .05n = 4.7\)
2) \(q + n = 30\)

So now you just need to solve for n.

\(q + n = 30\)
\(q = 30 - n\)

\(.25q + .05n = 4.7\)
\(.25(30-n) + .05n = 4.7\)
\(7.5 - .25n + .05n = 4.7\)
\(7.5 - .2n = 4.7\)
\(7.5 = 4.7 + .2n\)
\(7.5 - 4.7 = .2n\)
\(2.8 = .2n\)
\(2.8/.2 = n\)
\(14 = n\)

There are 14 nickels in the purse.

I picked a starting point and then kept ballparking until i hit the right answer

$4.70 - 6 quarters = $3.20. this would be 6 quarters and 64 nickels, WAY more than 30 so we need a lot more quarters

$4.70 - 16 quarters = $0.70 this would be 16 quarters and 14 nickels, 30 coins!

14 nickels!

Nickels ......................... Quarters ................ Total

0.05 ................................. 0.25 ................... 4.70 (Total Value)

x ................................... (30-x) ..................... 30 (Quantity)

Setting up the equation

0.05x + 0.25 (30-x) = 4.70

5x + 25(30-x) = 470

x + 5(30-x) = 94

x = 14

Answer = B

The average value of a coin is 4.70/30 =.157
So about 16 cents. That is 11 cents more than a nickel and 9 cents less than a quarter. If there were an equal numbers of quarters and nickels the average would come out to 15 cents a coin. There there are slightly more quarters than nickels. 14 is the only viable answer.

Posted from my mobile device

We can create the money equation::

25q + 5n = 470

5q + n = 94

And the coin equation:

n + q = 30

q = 30 - n

Substituting, we have:

5(30 - n) + n = 94

150 - 5n + n = 94

56 = 4n

14 = n

Answer: B
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Let the number of nickels be x

.05x + .25(30-x) = 4.7
7.5 - .2x = 4.7
x=14

IMO B

Posted from my mobile device
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